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Multiple symmetric positive solutions of a class of boundary value problems for higher order ordinary differential equations


Authors: John R. Graef, Chuanxi Qian and Bo Yang
Journal: Proc. Amer. Math. Soc. 131 (2003), 577-585
MSC (2000): Primary 34B15
DOI: https://doi.org/10.1090/S0002-9939-02-06579-6
Published electronically: June 18, 2002
MathSciNet review: 1933349
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Abstract: In this paper, the authors consider the boundary value problem \begin{gather} \tag {E} x^{(2m)}(t)+(-1)^{m+1} f(x(t))=0, \quad 0<t<1, \\ \tag {B} x^{(2i)}(0)=x^{(2i)}(1)=0, \quad i=0,1,2,\cdots ,m-1, \end{gather} and give sufficient conditions for the existence of any number of symmetric positive solutions of (E)–(B). The relationships between the results in this paper and some recent work by Henderson and Thompson (Proc. Amer. Math. Soc. 128 (2000), 2373–2379) are discussed.


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Additional Information

John R. Graef
Affiliation: Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, Tennessee 37403
Email: john-graef@utc.edu

Chuanxi Qian
Affiliation: Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762
Email: qian@math.msstate.edu

Bo Yang
Affiliation: Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762
Email: by2@ra.msstate.edu

Keywords: Boundary value problems, existence of positive solutions, higher order equations, multiple solutions, nonlinear equations
Received by editor(s): April 16, 2001
Received by editor(s) in revised form: October 2, 2001
Published electronically: June 18, 2002
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2002 American Mathematical Society